Quadratics By: Ou Suk Kwon

How can Factor Polynomials?

• In Algebra there are many ways to Factor the Polynomials, but the most common one is.

• First find any variable or number that can be solved by GCF. • Then multiply A and C, most of the time A is 1. • Then find 2 secret numbers that add up to B and multiply to

give the answer of A times C.• Then replace these 2 numbers over A.• Then simplify or reduce it.

Examples of Factoring Polynomials

• x^2+7x+10=0 A x C = 10 so we have to find 2 numbers that

add up to 7 and Multiply give us 10. So the answer for this one is +5 and +2. • x^2+10x+25=0 A x C = 25 and B= 10 so the answer is +5 and +5.• x^2+12x-45A x C =-45 and B= 12 so the answer is +15 and -3

Quadratic function • A quadratic function is a function that is shown in an

equation that is x=ax^2+bx+c. A never can equal to zero.

• The difference between a quadratic function and a linear function is that a linear graphs a line in the graph and the Quadratic functions graph a parabola in the graph.

differences:1. A quadratic function always has to be squared2. In linear function you are trying to find only one value

of variable, which is X. 3. The function of linear is y=mx+b and Quadratic is

Ax^2+bx+c.

Quadratic Function(Graph)• Your graphing formula always looks like A(x+B)

^2+C=0.A) A in the graph, always is going to be a slope of

the parabola. A is making the parabola to face down(-) or up(+). Also the value of the A changes the steepness of the parabola. If A > 0, then the parabola will be steeper, but when A < 0 then the parabola will be less steep.

B and C are the ones that changes the place of the vertex of the parabola. B is the value of X-axis and C is the value of Y-Axis.

B) As B changes in the X-axis, B changes the vertex to right or left. One thing that you have to be careful is that, B always changes to opposite way. When the value of B is negative, the vertex moves to right. B can be called P too.

C) C moves the vertex up or down, also C can be called Q.

Examples X^2

2(x-4)^2+3

Solving quadratics using graphing method

• The first thing that you must do is to put ax^2+bx+c equal to zero.

• Then make a T-table. • When you are making your t-table, you should found the

vertex first. To find the vertex you must use -B/2A this formula.

• After completing with the t-table, you must choose 2 points in the left to draw the same points in the right.

• After that, connect all the dots and make the parabola. The points that are on the X-axis, those are the answers of the quedratic.

Y=x^2

y=1/3x^2

Y=3x^2

Solving quadratic using square roots

• I guess solving quadratic using square root is the easiest way to solve the quadratics.

• In square roots you just have to add a square root sign to both sides of the equation

• And square root the variable and the number that has to be squared.

• Always remember about + and -

Examples • X^2=121x=11• X^2=4X=2• X^2=225X=15

Completing the square• Get x^2 = 1 • Then get C by itself• Complete the square• After that find (b/2)^2 and add to the both

sides of the equation.• Then simply square rood both sides, don’t

forget about + and -

Example• X^2+4x+10=2 X^2+4x=-8+4(X+2)^2=-8+4X+2=+-2X= -4, 0

• X^2+16x+6=16X^2+16x=10(x+4)^2=10+4X+4=+- root14X=-4-root14, -4+root14

• X^2+25x+4=8X^2+25x=4(X+5)^2=4+25/4X+5= +- 2root 25/4X=-5-2root 25/4, -5+2root 25/4

Solving Quadratic using the Formula.

• First think that you have to do in the formula is to find A, B, and C.

• When you found all of them, you should plug it in to these formula

Example • X^2+4x+6• A=1 B=4 C=6So -4+-root16-24/2• X^2+2x+5A=1 B=2 C=5So -2+-root4-20/2

• X^2+3x-2A=1 B=3 C=-2-3+-root9+8/2